New Textbooks in
Mathematics
Contents Algebra ..................................................................3 Discrete Mathematics/Combinatorics....................6 Differential Equations ..........................................13 General and Introductory Mathematics ..............14 Page 3
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Geometry & Topology ........................................17 Mathematical Modeling ......................................18 Mathematics for Finance......................................20 Algebraic Geometry and Number Theory ..........22 Numerical, Real, Complex and Functional Analysis ..............................................23 Math for Biology ..................................................26
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Mathematics for Engineers, Physicists, and Scientists ......................................................28 Probability and Operations Research ..................30
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MBTMTH1 TMC
Algebra
Finite-Dimensional Linear Algebra Mark S. Gockenbach Michigan Technological University, Houghton, USA Series: Discrete Mathematics and Its Applications
Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation.
Features:
The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces, including a brief introduction to functional analysis (infinite-dimensional linear algebra).
• Presents important concepts and methods from numerical linear algebra
Drawing on material from the author’s own course, this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.
Catalog no. K10803, 2010, 672 pp. ISBN: 978-1-4398-1563-2, $99.95
• Provides a thorough foundation for the study of advanced mathematics • Explores various applications of linear algebra, including polynomial interpolation, graph and coding theory, linear and integer programming, linear ordinary differential equations, Lagrange multipliers, and much more
• Contains a range of exercises in each section, including some that can be solved using a computer package such as MATLAB® • Incorporates mini-projects that encourage students to develop topics not covered in the text
Selected Table of Contents: Some Problems Posed on Vector Spaces Fields and Vector Spaces Linear Operators. Determinants and Eigenvalues The Jordan Canonical Form Orthogonality and Best Approximation The Spectral Theory of Symmetric Matrices The Singular Value Decomposition Matrix Factorizations and Numerical Linear Algebra Analysis in Vector Spaces Appendices Bibliography Index Solutions manual available with qualifying course adoptions
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Algebra Applied Algebra
Advanced Linear Algebra Bruce Cooperstein University of California, Santa Cruz, USA
Advanced Linear Algebra focuses on vector spaces and the maps between them that preserve their structure (linear transformations). It starts with familiar concepts and then slowly builds to deeper results. In addition to including many exercises and examples, each section reviews what students need to know before studying the material. The book first introduces vector spaces over fields as well as the fundamental concepts of linear combinations, span of vectors, linear independence, basis, and dimension. After covering linear transformations, it discusses the algebra of polynomials with coefficients in a field, concentrating on results that are consequences of the division algorithm. The author then develops the whole structure theory of a linear operator on a finite dimensional vector space from a collection of some simple results. He also explores the entire range of topics associated with inner product spaces, from the Gram–Schmidt process to the spectral theorems for normal and self-adjoint operators on an inner product space. The text goes on to rigorously describe the trace and determinant of linear operators and square matrices. The final two chapters focus on bilinear forms and tensor products and related material.
Codes, Ciphers and Discrete Algorithms, Second Edition Darel W. Hardy Colorado State University, Fort Collins, USA
Fred Richman Florida Atlantic University, Boca Raton, USA
Carol L. Walker New Mexico State University, Las Cruces, USA Series: Discrete Mathematics and Its Applications
“[T]he mathematics in the book are developed as needed and the focus of the book lies clearly on learning by examples and exercises. … the book gives good insight on how algebra can be used in coding and cryptography” —IACR Book Reviews, January 2010
Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes.
New to the Second Edition: • A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system
Designed for advanced undergraduate and beginning graduate students, this textbook shows students the beauty of linear algebra and prepares them for further study in mathematics.
• New appendix that reviews prerequisite topics in algebra and number theory
Selected Table of Contents
Selected Table of Contents
Vector Spaces. Linear Transformations. Polynomials. Theory of a Single Linear Operator. Inner Product Spaces. Linear Operators on Inner Product Spaces. Trace and Determinant of a Linear Operator. Bilinear Maps and Forms. Tensor Products. Appendices. Index.
Preface. Integers and Computer Algebra. Codes. Euclidean Algorithm. Ciphers. Error-Control Codes. Chinese Remainder Theorem. Theorems of Fermat and Euler. Public Key Ciphers. Finite Fields. Error-Correcting Codes. Advanced Encryption Standard. Polynomial Algorithms and Fast Fourier Transforms. Appendix. Solutions to Odd Problems. Bibliography. Notation. Algorithms. Figures. Tables. Index.
Catalog no. K11457, 2010, 364 pp. ISBN: 978-1-4398-2966-0, $79.95
• Double the number of exercises
Catalog no. C7142, 2009, 424 pp. ISBN: 978-1-4200-7142-9, $102.95
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Algebra Abstract Algebra An Interactive Approach William Paulsen Arkansas State University, Jonesboro, USA
A Modern Introduction to Linear Algebra Henry Ricardo
Series: Textbooks in Mathematics
Medgar Evers College, Brooklyn, New York, USA
By integrating the use of GAP and Mathematica®, Abstract Algebra: An Interactive Approach presents a hands-on approach to learning about groups, rings, and fields. Each chapter includes both GAP and Mathematica® commands, corresponding Mathematica® notebooks, traditional exercises, and several interactive computer problems that utilize GAP and Mathematica® to explore groups and rings.
"The single most exciting choice of this text is to start the semester with material on vectors (ndimensional real vectors). This allows for fast introduction to material that is new to students both to catch their interest and to demonstrate that this class deals with material that is very new to most of them. And it sets up the entire text for the proper perspective in higher level mathematics of having vectors as elements of spaces."
Although the book gives the option to use technology in the classroom, it does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many graduate-level topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. He also incorporates problem sequences that allow students to delve into interesting topics in depth, including Fermat’s two square theorem. This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area.
—Matthias Gobbert, University of Maryland
Selected Table of Contents Understanding the Group Concept. The Structure within a Group. Patterns within the Cosets of Groups. Mappings between Groups. Permutation Groups. Building Larger Groups from Smaller Groups. The Search for Normal Subgroups. Solvable and Insoluble Groups. Introduction to Rings. The Structure within Rings. Integral Domains and Fields. Unique Factorization. Finite Division Rings. The Theory of Fields. Galois Theory. Bibliography. Answers to Odd Problems. Index.
A Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. Concrete, easy-to-understand examples motivate the theory. The book first discusses vectors, Gaussian elimination, and reduced row echelon forms. It then offers a thorough introduction to matrix algebra, including defining the determinant naturally from the PA=LU factorization of a matrix. The author goes on to cover finite-dimensional real vector spaces, infinite-dimensional spaces, linear transformations, and complex vector spaces. The final chapter presents Hermitian and normal matrices as well as quadratic forms. Taking a computational, algebraic, and geometric approach to the subject, this book provides the foundation for later courses in higher mathematics. It also shows how linear algebra can be used in various areas of application. Although written in a "pencil and paper" manner, the text offers ample opportunities to enhance learning with calculators or computer usage.
Selected Table of Contents Vectors. Systems of Equations, Matrix Algebra. Eigenvalues, Eigenvectors, and Diagonalization. Vector Spaces. Linear Transformations. Inner Product Spaces. Hermitian Matrices and Quadratic Forms. Appendices. Answers/Hints to Odd-Numbered Problems. Index.
Solutions manual available for qualifying instructors Catalog no. C4521, 2010, 560 pp. ISBN: 978-1-4200-9452-7, $102.95
Solutions manual available for qualifying instructors Catalog no. K10040, 2010, 670 pp. ISBN: 978-1-4398-0040-9, $99.95
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Discrete Mathematics / Combinatorics
NEW
Introduction to Cryptography with Mathematical Foundations and Computer Implementations Alexander Stanoyevitch California State University–Dominguez Hills, Carson, USA Series: Discrete Mathematics and Its Applications
From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in cryptography, it delineates cryptographic concepts in chronological order, developing the mathematics as needed.
Features
Written in an engaging yet rigorous style, each chapter introduces important concepts with clear definitions and theorems. Numerous examples explain key points while figures and tables help illustrate more difficult or subtle concepts. Each chapter is punctuated with Exercises for the Reader; complete solutions for these are included in an appendix. Carefully crafted exercise sets are also provided at the end of each chapter, and detailed solutions to most odd-numbered exercises can be found in a designated appendix. The computer implementation section at the end of every chapter guides students through the process of writing their own programs. A supporting website provides an extensive set of sample programs as well as downloadable platform-independent applet pages for some core programs and algorithms.
• Presents algorithms in pseudo-code
As the reliance on cryptography by business, government, and industry continues and new technologies for transferring data become available, cryptography plays a permanent, important role in day-to-day operations. This self-contained sophomore-level text traces the evolution of the field, from its origins through present-day cryptosystems, including public key cryptography and elliptic curve cryptography.
Catalog no. K10916, January 2011, 669 pp. ISBN: 978-1-4398-1763-6, $89.95
• Provides a focused, self-contained treatment of cryptography • Covers elliptic curve cryptography • Offers complete coverage of all the needed material on number theory and abstract algebra
• Contains background material and extensive exercise solutions in the appendices • Includes both standard and computer exercises as well as numerous worked examples • Incorporates sample programs and platform-independent applets on www.csudh.edu/math/astanoyevitch/ cryptography.html
Selected Table of Contents An Overview of the Subject. Divisibility and Modular Arithmetic. The Evolution of Codemaking until the Computer Era. Matrices and the Hill Cryptosystem. The Evolution of Codebreaking until the Computer Era. Representation and Arithmetic of Integers in Different Bases. Block Cryptosystems and the Data Encryption Standard (DES). Some Number Theory and Algorithms. Public Key Cryptography. Finite Fields in General and GF(28) in Particular. The Advanced Encryption Standard (AES) Protocol. Elliptic Curve Cryptography. Appendixes. Exercises and Computer Implementations appear at the end of each chapter Solutions manual available for qualifying instructors
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Discrete Mathematics / Combinatorics
NEW
Discrete Structures with Contemporary Applications Alexander Stanoyevitch California State University–Dominguez Hills, Carson, USA
Reflecting many of the recent advances and trends in this area, Discrete Structures with Contemporary Applications covers the core topics in discrete structures as well as an assortment of novel applications-oriented topics. The applications described include simulations, genetic algorithms, network flows, probabilistic primality tests, public key cryptography, and coding theory.
Features
With clear definitions and theorems and carefully explained proofs, this classroom-tested text presents an accessible yet rigorous treatment of the material. Numerous worked-out examples illustrate key points while figures and tables help students grasp the more subtle and difficult concepts. Exercises for the Reader are interspersed throughout the text, with complete solutions included in an appendix. In addition, each section ends with extensive, carefully crafted exercise sets ranging from routine to nontrivial; answers can be found in an appendix. Most sections also contain computer exercises that guide students through the process of writing their own programs on any computing platform.
• Illustrates difficult concepts with more than 300 figures
Although the book highly encourages the use of computing platforms, it can be used without computers. The author explains algorithms in ordinary English and, when appropriate, in a natural and easy-to-understand pseudo code that can be readily translated into any computer language. A supporting website provides an extensive set of sample programs.
Catalog no. K10918, January 2011, 1002 pp. ISBN: 978-1-4398-1768-1, $99.95
• Covers many recent applications of discrete mathematics, including simulations, genetic algorithms, and public key cryptography • Presents algorithms in pseudo code • Offers sample programs via the author’s website
Pedagogical Features • Follows the recommendations of the ACM • Introduces several supplementary topics that can form an excellent basis for student projects • Includes a wide variety of examples and exercises, with solutions in the appendices • Incorporates computer exercises that teach students how to write their own programs
Selected Table of Contents Logic and Sets. Relations and Functions, Boolean Algebra, and Circuit Design. The Integers, Induction, and Recursion. Number Systems. Counting Techniques, Combinatorics, and Generating Functions. Discrete Probability and Simulation. Complexity of Algorithms. Graphs, Trees, and Associated Algorithms. Graph Traversal and Optimization Problems. Randomized Search and Optimization Algorithms. Appendices. References. Index. Solutions manual available for qualifying instructors
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Discrete Mathematics / Combinatorics
NEW
How to Count An Introduction to Combinatorics, Second Edition R.B.J.T. Allenby and Alan Slomson University of Leeds, UK Series: Discrete Mathematics and Its Applications
“[I]t’s the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its ‘naturalness’ is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya’s counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics.” —Paul Zeitz, University of San Francisco,
Completely revised, this text shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. They present proofs of key results as well as numerous worked examples. This second edition includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. It also contains 450 paired exercises, along with a full solution to one of the exercises in each pair.
Features • Explains combinatorial problems, from Fibonacci numbers, and the Königsberg bridges problem to the four-color problem, labeled trees, and card shuffling • Uses problems to introduce the theory • Contains enough material for a short course on graph theory • Presents proofs of key results as well as numerous worked examples • Includes paired exercises, along with a full solution to one of the exercises in each pair • Lists suggestions for further reading
Selected Table of Contents What’s It All About?. Permutations and Combinations. Occupancy Problems. The Inclusion-Exclusion Principle. Stirling and Catalan Numbers. Partitions and Dot Diagrams. Generating Functions and Recurrence Relations. Partitions and Generating Functions. Introduction to Graphs. Trees. Groups of Permutations. Group Actions. Counting Patterns. Pólya Counting. Dirichlet’s Pigeonhole Principle. Ramsey Theory. Rook Polynomials and Matchings. Solutions to the A Exercises. Books for Further Reading. Index. Solutions manual available for qualifying instructors
Catalog no. C8260, January 2011, 444 pp. ISBN: 978-1-4200-8260-9, $79.95
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Discrete Mathematics / Combinatorics
NEW
Introduction to Combinatorics W.D. Wallis Southern Illinois University, Carbondale, USA
J.C. George Gordon College, Barnesville, Georgia, USA Series: Discrete Mathematics and Its Applications
Accessible to undergraduate students, Introduction to Combinatorics presents approaches for solving counting and structural questions. It looks at how many ways a selection or arrangement can be chosen with a specific set of properties and determines if a selection or arrangement of objects exists that has a particular set of properties. To give students a better idea of what the subject covers, the authors first discuss several examples of typical combinatorial problems. They also provide basic information on sets, proof techniques, enumeration, and graph theory—topics that appear frequently throughout the book. The next few chapters explore enumerative ideas, including the pigeonhole principle and inclusion/exclusion. The text then covers enumerative functions and the relations between them. It describes generating functions and recurrences, important families of functions, and the theorems of Pólya and Redfield. The authors also present introductions to computer algebra and group theory before considering structures of particular interest in combinatorics: graphs, codes, Latin squares, and experimental designs. The last chapter further illustrates the interaction between linear algebra and combinatorics. Exercises and problems of varying levels of difficulty are included at the end of each chapter. Ideal for undergraduate students in mathematics taking an introductory course in combinatorics, this text explores the different ways of arranging objects and selecting objects from a set. It clearly explains how to solve the various problems that arise in this branch of mathematics.
Features • Covers key families of functions, including Catalan, Bell, and Stirling numbers • Explains graph theory, coding theory, and design theory • Illustrates traditional problems with modern examples, such as digital music tracks • Discusses Maple™, Mathematica®, and other technological tools where appropriate • Provides several appendices that offer background material on sets, induction, proof techniques, vectors, and matrices as well as brief biographies of mathematicians relevant to the topics • Includes exercises and problems in each chapter, with some solutions at the back of the book
Selected Table of Contents Introduction. Fundamentals of Enumeration. The Pigeonhole Principle and Ramsey’s Theorem. The Principle of Inclusion and Exclusion. Generating Functions and Recurrence Relations. Catalan, Bell and Stirling Numbers. Symmetries and the Pólya–Redfield Method. Introduction to Graph Theory. Further Graph Theory. Coding Theory. Latin Squares. Balanced Incomplete Block Designs. Linear Algebra Methods in Combinatorics. Appendices. Solutions to Set A Exercises. Hints for Problems. Solutions to Problems. References. Index.
Catalog no. K10310, January 2011, 397 pp. ISBN: 978-1-4398-0622-7, $79.95
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Discrete Mathematics / Combinatorics
NEW
Graphs & Digraphs Fifth Edition Gary Chartrand and Ping Zhang Western Michigan University, Kalamazoo, USA
Linda Lesniak Drew University, Madison, New Jersey, USA
New to the Fifth Edition • New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings • New examples, figures, and applications to illustrate concepts and theorems • Expanded historical discussions of wellknown mathematicians and problems • More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book
Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics.
Selected Table of Contents Introduction to Graphs Trees and Connectivity Eulerian and Hamiltonian Graphs Digraphs
• Reorganization of sections into subsections to make the material easier to read
Graphs: History and Symmetry
• Bolded definitions of terms, making them easier to locate
Graph Embeddings
Planar Graphs Vertex Colorings
Praise for the Fourth Edition “… a popular point of entry to the field … has evolved with the field from a purely mathematical treatment to one that also addresses the needs of computer scientists.” —L’Enseignement Mathématique
“… emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge … For 25 years, Graphs & Digraphs, in its various editions, has served as an exemplary introduction to the emerging mathematical disciplines of graph theories, for advanced undergraduate and graduate students. It has also served established graph theorists, combinatorialists, and other discrete mathematicians, as well as computer scientists and chemists, as a useful reference work. The fourth edition continues these fine traditions.“ —Zentralblatt MATH
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Map Colorings Matchings, Factorization, and Domination Edge Colorings Extremal Graph Theory Hints and Solutions to Odd-Numbered Exercises Bibliography Indices List of Symbols
Catalog no. K11263, January 2011, 598 pp. ISBN: 978-1-4398-2627-0, $89.95
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Discrete Mathematics / Combinatorics
Discrete Mathematics Proofs, Structures and Applications, Third Edition Rowan Garnier Surrey, UK
John Taylor University of Brighton, UK
"This is a textbook on discrete mathematics for undergraduate students in computer science and mathematics. The choice of the topics covered in this text is largely suggested by the needs of computer science. It contains chapters on set theory, logic, algebra (matrix algebra and Boolean algebra), and graph theory with applications. … The style of exposition is very clear, step by step and the level is well adapted to undergraduates in computer science. The treatment is mathematically rigorous; therefore it is also suitable for mathematics students. Besides the theory there are many concrete examples and exercises (with solutions!) to develop the routine of the student. So I can recommend warmly this book as a textbook for a course. It looks very attractive and has a nice typography. …I think it is an excellent textbook." —H.G.J. Pijls, University of Amsterdam, The Netherlands
Selected Table of Contents Logic Mathematical Proof Sets Relations Functions Matrix Algebra Systems of Linear Equations Algebraic Structures Introduction to Number Theory Boolean Algebra Graph Theory Applications of Graph Theory References and Further Reading Hints and Solutions to Selected Exercises Index
New to the Third Edition In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors.
Catalog no. K10650, 2010, 843 pp. ISBN: 978-1-4398-1280-8, $89.95
Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the everevolving discipline of computer science.
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Discrete Mathematics / Combinatorics
Applied Combinatorics Second Edition Fred Roberts Rutgers University, Piscataway, New Jersey, USA
Barry Tesman Dickinson College, Carlisle, PA, USA
“This book is a required textbook for my graduate course in discrete mathematics. Both my students and I have found it to be an excellent resource with interesting application examples from a variety of fields interspersed throughout the text. The book is very well organized and clearly reinforces both the practical and theoretical understanding in a way students are able to correlate. Because the level of difficulty for selected problems range from simple to challenging, it makes an appropriate text for junior, senior, and graduate students alike. I am particularly pleased with the relevancy and inclusion of computer science applications” —Dawit Haile, Virginia State University, Petersburg, USA
“The writing style is excellent. … The explanations are detailed enough that the students can follow the arguments readily. The motivating examples are a truly strong point for the text. No other text with which I am familiar comes even close to the number of applications presented here” —John Elwin, San Diego State University, California, USA
“Roberts and Tesman’s book covers all the major areas of combinatorics in a clear, insightful fashion. But what really sets it apart is its impressive use of applications. I know of no other text which comes close. There are entire sections devoted to subjects like computing voting power, counting organic compounds built up from benzene rings, and the use of orthogonal arrays in cryptography. And in exercises and examples, students test psychic powers, consider the UNIX time problem, plan mail carriers’ routes, and assign state legislators to committees. This really helps them to understand the mathematics and also to see how this field is useful in the real world.”
Now with solutions to selected problems, this bestselling textbook presents the tools of combinatorics from an applied point of view. It offers many examples from the biological, computer, and social sciences as well as numerous references to the literature of combinatorics and its applications that enable readers to delve more deeply into the topics.
Selected Table of Contents What Is Combinatorics? THE BASIC TOOLS OF COMBINATORICS: Basic Counting Rules Introduction to Graph Theory Relations THE COUNTING PROBLEM: Generating Functions and Their Applications Recurrence Relations The Principle of Inclusion and Exclusion The Pólya Theory of Counting THE EXISTENCE PROBLEM: Combinatorial Designs Coding Theory Existence Problems in Graph Theory COMBINATORIAL OPTIMIZATION: Matching and Covering Optimization Problems for Graphs and Networks Appendix Indices
—Thomas Quint, University of Nevada, Reno, USA
Catalog no. K10016, 2009, 848 pp. ISBN: 978-1-4200-9982-9, $99.95
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Differential Equations Ordinary Differential Equations Applications, Models, and Computing Charles E. Roberts Indiana State University, Terre Haute, USA
Solution Techniques for Elementary Partial Differential Equations Second Edition Christian Constanda
Series: Textbooks in Mathematics
Roberts gives a clear, detailed introduction to ordinary differential equations for students who have completed the full calculus sequence. … the book’s exercises and examples … are independent of any particular software—a very nice feature. Roberts provides a good balance between theoretical and applied material. … The work is very readable and offers instructors much material to work with in their courses. Summing Up: Recommended. —CHOICE, December 2010
Bringing the computer into the classroom, this text emphasizes the use of computer software in teaching linear and nonlinear differential equations and systems. Along with discussing fundamental existence, uniqueness, and continuation theorems, it includes numerical case studies that highlight possible pitfalls when computing a numerical solution without first considering the appropriate theory. Requiring no prior knowledge of programming languages, the text shows how to solve various mathematical models, such as population growth, epidemic, and predator-prey models. The accompanying CD-ROM contains the software programs used in the text.
Selected Table of Contents The Initial Value Problem y′ = f (x, y); y(c) =d. Applications of the Initial Value Problem y′ = f (x, y); y(c) =d. N-th Order Linear Differential Equations. The Laplace Transform Method. Applications of Linear Differential Equations with Constant Coefficients. Linear Systems of FirstOrder Differential Equations. Applications of Linear Systems with Constant Coefficients. Applications of Systems of Equations. A solutions manual is available for qualifying instructors Catalog no. K11006, 2010, 600 pp. ISBN: 978-1-4398-1908-1, $99.95
University of Tulsa, Oklahoma, USA Series: Chapman Hall/CRC Mathematics Series
"This concise, well-written book, which includes a profusion of worked examples and exercises, serves both as an excellent text in undergraduate and graduate learning and as a useful presentation of solution techniques for researchers and engineers interested in applying partial differential equations to real-life problems." —Barbara Zubik-Kowal, Boise State University, Idaho, USA
This popular text presents some of the most important and widely used methods for solving PDEs. Along with a new chapter on complex variable methods, this edition includes new sections on Cauchy–Euler equations, Bessel functions, Legendre polynomials, spherical harmonics, applications of Fourier transformations, and general hyperbolic equations. It lists additional mathematical models based on PDEs and shows how the methods of separation of variables and eigenfunction expansion work for equations other than heat, wave, and Laplace. The author also added many new worked examples and exercises.
Selected Table of Contents Ordinary Differential Equations: Brief Revision. Fourier Series. Sturm–Liouville Problems. Some Fundamental Equations of Mathematical Physics. The Method of Separation of Variables. Linear Nonhomogeneous Problems. The Method of Eigenfunction Expansion. The Fourier Transformations. The Laplace Transformation. The Method of Green’s Functions. General Second-Order Linear Partial Differential Equations with Two Independent Variables. The Method of Characteristics. Perturbation and Asymptotic Methods. Complex Variable Methods. Answers to Odd-Numbered Exercises. Appendix. Bibliography. Index. Ancillary materials are available for qualifying instructors Catalog no. K10569, 2010, 343 pp., Soft Cover ISBN: 978-1-4398-1139-9, $69.95
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General and Introductory Mathematics
NEW
NEW
A Mathematical Look at Politics
Mathematics for the Environment
E. Arthur Robinson, Jr. and Daniel H. Ullman George Washington University, Washington, District of Columbia, USA
What Ralph Nader's spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Dean’s method. How the U.S. tried to use game theory to win the Cold War, and why it didn’t work. When students realize that mathematical thinking can address these sorts of pressing concerns of the political world it naturally sparks their interest in the underlying mathematics. A Mathematical Look at Politics is designed as an alternative to the usual mathematics texts for students in quantitative reasoning courses. It applies the power of mathematical thinking to problems in politics and public policy. Concepts are precisely defined, and hypotheses are laid out. Propositions, lemmas, theorems, and corollaries are stated and proven. Counterexamples are offered to refute conjectures. Students are expected not only to make computations but also to state results, prove them, and draw conclusions about specific examples.
Martin Walter University of Colorado, Boulder, USA
Mathematics for the Environment shows how to employ simple mathematical tools, such as arithmetic, to uncover fundamental conflicts between the logic of human civilization and the logic of Nature. These tools can then be used to understand and effectively deal with economic, environmental, and social issues. With elementary mathematics, the book seeks answers to a host of real-life questions, including: • How safe is our food and will it be affordable in the future? • What are the simple lessons to be learned from the economic meltdown of 2008–2009? • Is global climate change happening? • Were some humans really doing serious mathematical thinking 50,000 years ago? • What does the second law of thermodynamics have to do with economics? • How can identity theft be prevented?
Selected Table of Contents
• What does a mathematical proof prove?
Preface, for the Student. Preface, for the Instructor. Voting. Two Candidates. Social Choice Functions. Criteria for Social Choice. Which Methods are Good? Arrow's Theorem. Variations on the Theme. Notes on Part I. Apportionment. Hamilton's Method. Divisor Methods. Criteria and Impossibility. The Method of Balinski and Young. Deciding Among Divisor Methods. History of Apportionment in the United States. Notes on Part II. Conflict. Strategies and Outcomes. Chance and Expectation. Solving Zero-Sum Games. Conflict and Cooperation. Nash Equilibria. The Prisoner's Dilemma. Notes on Part III. The Electoral College. Weighted Voting. Whose Advantage? Notes on Part IV. Solutions to Odd-Numbered Exercises and Problems. Bibliography. Index.
A truly interdisciplinary, concrete study of mathematics, this classroom-tested text discusses the importance of certain mathematical principles and concepts, such as fuzzy logic, feedback, deductive systems, fractions, and logarithms, in various areas other than pure mathematics. It teaches students how to make informed choices using fundamental mathematical tools, encouraging them to find solutions to critical real-world problems.
Catalog no. K11044, January 2011, 477 pp. ISBN: 978-1-4398-1983-8, $49.95
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Selected Table of Contents Mathematics Is Connected to Everything Else. Math and Nature: The Nature of Math. One of the Oldest Mathematical Patterns. Counting. Box Models: Population, Money, Recycling. Chance: Health, Surveillance, Spies, and Voting. Economics. Media Literacy. References. Index. Catalog no. K11565, January 2011, 679 pp. ISBN: 978-1-4398-3472-5, $89.95
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General and Introductory Mathematics NEW
Mathematics in Games, Sports, and Gambling
A Concise Introduction to Pure Mathematics
The Games People Play
Third Edition
Ronald J. Gould
Martin Liebeck
Emory University, Atlanta, Georgia, USA
Imperial College, London, UK “This book displays a unique combination of
lightness and rigor, leavened with the right dose of humor. When I used it for a course, students could not get enough, and I have been recommending independent study from it to students wishing to take a core course in analysis without having taken the prerequisite course. The material is very well chosen and arranged, and teaching from Liebeck’s book has in many different ways been among my most rewarding teaching experiences during the last decades.” —Boris Hasselblatt, Tufts University, Medford, Massachusetts, USA
"In addition to preparing students to go on in mathematics, it is also a wonderful choice for a student who will not necessarily go on in mathematics but wants a gentle but fascinating introduction into the culture of mathematics. … This book will give a student the understanding to go on in further courses in abstract algebra and analysis. The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. At the very least, the student will have an appreciation of mathematics. As usual, Liebeck’s writing style is clear and easy to read. This is a book that could be read by a student on his or her own. There is a wide selection of problems ranging from routine to quite challenging.” —From the Foreword
Selected Table of Contents Sets and Proofs. Number Systems. Decimals. Inequalities. nth Roots and Rational Powers. Complex Numbers. Polynomial Equations. Induction. Euler’s Formula and Platonic Solids. The Integers. Prime Factorization. More on Prime Numbers. Congruence of Integers. More on Congruence. Secret Codes. Counting and Choosing. More on Sets. Equivalence Relations. Functions. Permutations. Infinity. Introduction to Analysis: Bounds. More Analysis: Limits. Yet More Analysis: Continuity. Solutions to Odd-Numbered Exercises. Further Reading. Index of Symbols. Index. Catalog no. K11624, January 2011, 268 pp. Soft Cover, ISBN: 978-1-4398-3598-2 $59.95
Winner of 2011 CHOICE Outstanding Academic Title “…this volume is a wonderful reference for studying probability or statistics … Though this book might serve as the seed for the development of a new mathematics course at some institutions, this reviewer sees its greater value as a reference for mathematicians who are unfamiliar with the probabilities associated with gambling or applying statistics in sports.” —J.T. Noonan, Mount Vernon Nazarene University
Mathematics in Games, Sports, and Gambling: The Games People Play shows how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. It draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games. Requiring only high school algebra, the text offers flexibility in choosing what material to cover in a basic mathematics course. It covers permutations in the two-deck matching game, introduces graphs to find matches when looking at extensions of the five-card trick, and studies lexicographic orderings and ideas of encoding for card tricks. The text explores linear equations and weighted equations in the section on the NFL passer rating formula and presents graphing to show how data can be compared or displayed. For each topic, the author includes exercises based on real games and sports data.
Selected Table of Contents Basic Probability. The Game’s Afoot. Repeated Play. Card Tricks and More. Dealing with Data. Testing and Relationships. Games and Puzzles. Combinatorial Games. Appendix. References. Index. Catalog no. K10099, 2010, 374 pp. ISBN: 978-1-4398-0163-5, $61.95
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General and Introductory Mathematics Introduction to Mathematical Logic
Introduction to Mathematical Proofs
Fifth Edition
A Transition
Elliott Mendelson
Charles E. Roberts, Jr.
Queens College, Flushing, New York, USA
Indiana State University, Terre Haute, USA
Series: Discrete Mathematics and Its Applications, Vol. 48
Series: Textbooks in Mathematics
“Since it first appeared in 1964, Mendelson's book has been recognized as an excellent textbook in the field. It is one of the most frequently mentioned texts in references and recommended reading lists … This book rightfully belongs in the small, elite set of superb books that every computer science graduate, graduate student, scientist, and teacher should be familiar with.”
Introduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills necessary to write clear, correct, and concise proofs.
—Computing Reviews, May 2010
"Since its first edition, this fine book has been a text of choice for a beginner’s course on mathematical logic. … There are many fine books on mathematical logic, but Mendelson’s textbook remains a sure choice for a first course for its clear explanations and organization: definitions, examples and results fit together in a harmonic way, making the book a pleasure to read. The book is especially suitable for self-study, with a wealth of exercises to test the reader’s understanding." —MAA Reviews, December 2009
Retaining all the key features of its predecessors, this fifth edition of a long-established, bestselling text explores the principal topics of mathematical logic. It includes a new section covering basic ideas and results about nonstandard models of number theory, a second appendix that introduces modal propositional logic, an expanded bibliography, and additional exercises and selected answers. This edition continues to cover propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. It also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.
Selected Table of Contents The Propositional Calculus. First-Order Logic and Model Theory. Formal Number Theory. Axiomatic Set Theory. Computability. Appendices. Answers to Selected Exercises. Bibliography. Notation. Index.
Unlike similar textbooks, this one begins with logic, since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It will prepare them to succeed in more advanced mathematics courses, such as abstract algebra and geometry.
Selected Table of Contents Logic. Deductive Mathematical Systems and Proofs. Set Theory. Relations. Functions. Mathematical Induction. Cardinalities of Sets. Proofs from Group Theory. Appendix. Answers to Selected Exercises. References. Index. Solutions manual available for qualifying instructors Catalog no. C6955, 2009, 433 pp. ISBN: 978-1-4200-6955-6, $92.95
Catalog no. C8768, 2010, 469 pp. ISBN: 978-1-58488-876-5, $89.95
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Geometry and Topology
Essentials of Topology with Applications Washington University, St. Louis, Missouri, USA
Differential Geometry of Curves and Surfaces
Series: Textbooks in Mathematics
Thomas F. Banchoff and Stephen T. Lovett
Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories.
Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces and one- and twodimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties.
Steven G. Krantz
After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in a number of areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures.
Features • Imparts a clear, solid understanding of modern topology • Contains material on graph theory and dynamical systems, both of which are insightful applications of topological ideas • Offers numerous examples, illustrations, and exercises to make learning the topic easier • Includes several appendices that supply background information on logic, real variable theory, set theory, and algebraic structures
A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
Selected Table of Contents Plane Curves: Local Properties Plane Curves: Global Properties Curves in Space: Local Properties Curves in Space: Global Properties Regular Surfaces The First and Second Fundamental Forms The Fundamental Equations of Surfaces Curves on Surfaces Catalog no. K00382, 2010, 352 pp. ISBN: 978-1-56881-456-8, $49.00
Selected Table of Contents Fundamentals. Advanced Properties of Topological Spaces. Basic Algebraic Topology. Manifold Theory. Moore–Smith Convergence and Nets. Function Spaces. Knot Theory. Graph Theory. Dynamical Systems. Appendices. Solutions of Selected Exercises. Bibliography. Index. Catalog no. C9749, 2010, 420 pp. ISBN: 978-1-4200-8974-5, $89.95
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Geometry and Topology
Differential Geometry of Manifolds Stephen Lovett “We live in an age when borders between mathematical disciplines (and even between parts of mathematics and parts of physics) are being redrawn --or erased altogether-- and differential geometry is a major player in all this Perestroika. Thus, the teaching of the subject to rookies should perhaps be restructured, too, at least in the sense of getting to the more avant garde stuff more quickly, and it looks like a major aim of Lovett's book is exactly that. ... I think this is going to be a very successful textbook especially for rookie graduate students (and the zealous undergraduate would-be differential geometer, of course), as well as a very popular self-study source. It is a very nice book indeed.” —Michael Berg, Professor of Mathematics, Layola Marymount University, Los Angeles, CA.
Assuming only prior knowledge of multivariable calculus and linear algebra, this book introduces classical differential geometry of curves and surfaces and proceeds seamlessly to the modern theory of manifolds. The first part introduces the local and global theories of plane curves and then space curves. The middle studies the extrinsic and intrinsic geometry of regular surfaces, including the Theorema Egregium and the Gauss-Bonnet Theorem. The final chapters develop the notion of a differentiable manifold, study Riemannian manifolds and conclude with applications of manifolds to physics.
Selected Table of Contents Analysis of Multivariable Functions. Coordinates, Frames, and Tensor Notation. Differentiable Manifolds. Analysis on Manifolds. Introduction to Riemannian Geometry. Applications of Manifolds to Physics. Point Set Topology. Calculus of Variations. Multilinear Algebra. Catalog no. K00383, 2010, 440 pp. ISBN: 978-1-56881-457-5, $79.00
Mathematical Modeling
Mathematical and Experimental Modeling of Physical and Biological Processes H.T. Banks and H.T. Tran North Carolina State University, Raleigh, USA
“…would I buy this textbook? Again, absolutely yes! The concise and clear style in which the background is written for each chapter will be invaluable as a quick, ‘before the lecture is given’ refresher. … Most of the topics covered are those which have arisen out of the research projects that the authors have conducted themselves. This is the kind of hands-on experience that a lecturer would need in order to make the laboratory experiences for the students enjoyable and rewarding.” —Mathematical Reviews, Issue 2010
“The aim of this book is twofold: to develop some standard models of physical and biological processes (the transport equation, heat conduction, the beam equation, fluid dynamics, and structured population models) in mathematical language, and probably more importantly, to show how and why to design concrete engineering experiments for comparing numerical results of models with specific experimental data. … The book can be recommended to advanced undergraduate students for whom mathematics is a bit more than just proving theorems.” —EMS Newsletter, September 2009
Exploring how mathematics is applied to problems in science and engineering, this book explains physical and biological relationships and mechanisms through a principles-based fundamental modeling approach, emphasizing model validation through specific laboratory experiments as well as data collection and analysis. It covers thermal imaging and detection, dynamic properties of beams, acoustics and fluid transport, and size-structured population dynamics for marine populations.
Selected Table of Contents Introduction: The Iterative Modeling Process. Modeling and Inverse Problems. Mathematical and Statistical Aspects of Inverse Problems. Mass Balance and Mass Transport. Heat Conduction. Structural Modeling: Force/Moments Balance. Beam Vibrational Control and Real-Time Implementation. Wave Propagation. SizeStructured Population Models. Appendices. Catalog no. C7337, 2009, 298 pp. ISBN: 978-1-4200-7337-9, $82.95
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Mathematical Modeling
Stochastic Financial Models Douglas Kennedy Trinity College, Cambridge, UK Series: Chapman & Hall/CRC Financial Mathematics Series
"This book is a superb beginning level text for senior undergraduate/graduate mathematicians, which is based on lectures delivered by its author to many generations of appreciative Cambridge mathematicians. Many of my own Ph.D. and masters students have taken Dr. Kennedy’s course to uniformly good reviews; this readable book will make its material available to a worldwide audience. ...the book contains 40 pages of fully worked out solutions to help introduce the reader to the Oxbridge style of learning by problem solving in which even supervisors are sometimes challenged." —Michael A.H. Dempster, Centre for Financial Research, Statistical Laboratory, University of Cambridge, UK
Filling the void between surveys of the field with relatively light mathematical content and books with a rigorous, formal approach to stochastic integration and probabilistic ideas, Stochastic Financial Models provides a sound introduction to mathematical finance. The author takes a classical applied mathematical approach, focusing on calculations rather than seeking the greatest generality. Developed from the esteemed author’s advanced undergraduate and graduate courses at the University of Cambridge, the text begins with the classical topics of utility and the mean-variance approach to portfolio choice. The remainder of the book deals with derivative pricing. The author fully explains the binomial model since it is central to understanding the pricing of derivatives by selffinancing hedging portfolios. He then discusses the general discrete-time model, Brownian motion and the Black–Scholes model. The book concludes with a look at various interest-rate models. Concepts from measure-theoretic probability and solutions to the end-of-chapter exercises are provided in the appendices. By exploring the important and exciting application area of mathematical finance, this text encourages students to learn more about probability, martingales and stochastic integration.
Features • Presents a self-contained treatment of mathematical models in finance by including the relevant mathematical background • Takes a hands-on approach to calculations, enabling students to derive the prices of many common financial products • Assumes no prior knowledge of stochastic calculus or measure-theoretic probability
Selected Table of Contents Portfolio Choice Introduction. Utility. Mean-variance analysis. The Binomial Model One-period model. Multi-period model. A General Discrete-Time Model One-period model. Multi-period model. Brownian Motion Introduction. Hitting-time distributions. Girsanov’s theorem. Brownian motion as a limit. Stochastic calculus. The Black–Scholes Model Introduction. The Black–Scholes formula. Hedging and the Black–Scholes equation. Pathdependent claims. Dividend-paying assets. Interest-Rate Models Introduction. Survey of interest-rate models. Gaussian random-field model. Appendices Mathematical Preliminaries. Solutions to the Exercises. Further Reading. References. Index. Exercises appear at the end of each chapter.
Catalog no. C3452, 2010, 264 pp. ISBN: 978-1-4200-9345-2, $69.95
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Mathematics for Finance Interest Rate Modeling Theory and Practice
Portfolio Optimization Michael J. Best University of Waterloo, Ontario, Canada
Eschewing a more theoretical approach, Portfolio Optimization shows how the mathematical tools of linear algebra and optimization can quickly and clearly formulate important ideas on the subject. This practical book extends the concepts of the Markowitz "budget constraint only" model to a linearly constrained model. It explains how the basic portfolio optimization problem can help determine the optimal investment of an investor’s wealth in each asset owned.
Features • Extends the key ideas of the Markowitz “budget constraint only” model to a model having linear inequality constraints • Develops the key ideas of portfolio optimization using only elementary linear algebr • Tackles a wide range of derivative approaches • Demonstrates how to apply the linearly constrained model, today’s practitioners insist upon • Explores all the quadratic programming essential to solving practical portfolio problems • Works out fundamental problems by hand but provides the MATLAB software needed for continued problem solving • Explains how to use MATLAB programs included on CD-ROM • Includes exercises at the end of each chapter
Selected Table of Contents Optimization. The Efficient Frontier. The Capital Asset Pricing Model. Sharpe Ratios and Implied Risk-Free Returns. Quadratic Programming Geometry. A QP Solution Algorithm. Portfolio Optimization with Linear Inequality Constraints. Determination of the Entire Efficient Frontier. Sharpe Ratios under Constraints and Kinks. Appendix. References.
Lixin Wu University of Science & Technology, Kowloon, Hong Kong Series: Chapman & Hall/CRC Financial Mathematics Series, Vol. 15
Containing many results that are new or exist only in recent research articles, this text portrays the theory of interest rate modeling as a threedimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods. Taking a top-down approach, the author shows readers how to build and use models. The text includes exercises and real-world examples, along with code, tables, and figures accessible on the author’s website.
Features • Presents a complete cycle of model construction and applications, showing readers how to build and use models • Incorporates high-power numerical methodologies • Provides a systematic treatment of intriguing industrial issues, such as volatility and correlation adjustments • Contains exercise sets and a number of examples, with many based on real market data • Includes comments on cutting-edge research, such as volatility-smile, positive interest-rate models, and convexity adjustment • Offers code, tables, and figures on the author’s website
Selected Table of Contents The Basics of Stochastic Calculus. The Martingale Representation Theorem. Interest Rates and Bonds. The Heath–Jarrow–Morton Model. ShortRate Models and Lattice Implementation. The LIBOR Market Model. Calibration of LIBOR Market Model. Volatility and Correlation Adjustments. Affine Term Structure Models. References. Index.
Along with end-of-chapter exercises, the text includes MATLAB® to help with problem solving and offers the programs on a CD-ROM. A solutions manual is available for qualifying instructors.
A solutions manual is available for qualifying instructors
Catalog no. C5840, 2010, 236 pp. ISBN: 978-1-4200-8584-6, $79.95
Catalog no. C0569, 2009, 353 pp. ISBN: 978-1-4200-9056-7, $82.95
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Mathematics for Finance NEW
Stochastic Finance A Numeraire Approach Jan Vecer
Introduction to Financial Models for Management and Planning
Columbia University , New York, New York, USA
James R. Morris and John P. Daley
Series: Chapman & Hall/CRC Financial Mathematics, Vol. 20
University of Colorado, Denver, USA
“Although the importance of the choice of numeraire has been recognized for quite some time, this is the first book to stress the fundamental role that numeraires play in modern asset pricing theory. The author is the leading expert on the subject so it is a pleasure to highly recommend this book.”
This text provides graduate level instruction on the development of models for financial management and planning. By working through the problems and models in this text, readers will learn how computer based models should be structured to analyze a firm’s investment and financing. The authors emphasize modeling problems related to financial management, firm valuation, forecasting, and security pricing. Monte Carlo simulation is emphasized and access to the Monte Carlo simulation software @Risk is included with the text.
—Peter Carr, Ph.D., Managing Director of Morgan Stanley and Executive Director of NYU’s Masters in Math Finance
“Finally, we have a full volume with a systematic treatment of the change of numeraire techniques. Jan Vecer has taken years of teaching experience and practitioners’ feedback to unify a previously complicated topic into the most elegant and easily accessible numeraire textbook to come down the pike. Now it has become fun to learn about parity and duality relationships among exotic options in a whole variety of models. The practitioners will be happy about the dimension reduction methods. There should be more such books.” —Uwe Wystup, Ph.D., Managing Director of MathFinance AG
This classroom-tested text provides a deep understanding of derivative contracts. Unlike much of the existing literature, the book treats price as a number of units of one asset needed for an acquisition of a unit of another asset instead of expressing prices in dollar terms exclusively. This numeraire approach leads to simpler pricing options for complex products, such as barrier, lookback, quanto, and Asian options. With many examples and exercises, the text relies on intuition and basic principles, rather than technical computations.
Selected Table of Contents Introduction. Elements of Finance. Binomial Model. Diffusion Models. Interest Rate Contracts. Barrier Options. Lookback Options. American Options. Contracts on Three or More Assets: Quantos, Rainbows and "Friends". Asian Options. Jump Models. Appendix. Solutions to Selected Exercises. References. Index.
Features • Covers all key aspects of financial modeling • Introduces powerful tools for the financial toolbox • Contains extensive exercises throughout the text • Provides complementary access to Monte Carlo simulation software • Solutions manual and PowerPoint® lectures Placing a strong emphasis on the structure of models, the book focuses on developing models that are consistent with the theory of finance and, at the same time, are practical and usable. The authors introduce powerful tools that are imperative to the financial management of the operating business. These include interactive cash budgets and pro forma financial statements that balance even under the most extreme assumptions, valuation techniques, forecasting techniques that range from simple averages to time series methods, Monte Carlo simulation, linear programming, and optimization. Catalog no. C0542, 2009, 754 pp. ISBN: 978-1-4200-9054-3, $92.95
Catalog no. K10632, January 2011, 342 pp. ISBN: 978-1-4398-1250-1, $69.95
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Algebraic Geometry and Number Theory Advanced Number Theory with Applications
NEW
Richard A. Mollin
Richard A. Mollin
University of Calgary, Alberta, Canada
University of Calgary, Alberta, Canada
Series: Discrete Mathematics and Its Applications
Series: Discrete Mathematics and Its Applications
“This terrific book is testimony to Richard Mollin’s mathematical erudition, wonderful taste, and also his breadth of culture. … Mollin’s treatment of elliptic curves is a model of clear exposition … [It] succeeds very well in its goal of providing a means of transition from more or less foundational material to papers and advanced monographs, i.e., research in the field. … a wondrous book, successfully fulfilling the author’s purpose of effecting a bridge to modern number theory for the somewhat initiated. … it’s very nice to find in Mollin’s book a high quality and coherent treatment of this beautiful material and pointers in abundance to where to go next.”
Praise for the First Edition
—Michael Berg, Loyola Marymount University, MAA Review, 2009
By covering a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory, this text provides the most up-to-date and comprehensive material for a second course in this field. With numerous examples and exercises, it begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes. The author then applies these tools to Diophantine equations before developing elliptic curves and modular forms. He also presents Fermat’s Last Theorem, the ABC conjecture, and sieve methods.
Selected Table of Contents Algebraic Number Theory and Quadratic Fields . Ideals. Binary Quadratic Forms. Diophantine Approximation. Arithmetic Functions. Introduction to p-Adic Analysis. Dirichlet: Characters, Density, and Primes in Progression. Applications to Diophantine Equations. Elliptic Curves. Modular Forms. Appendix: Sieve Methods. Bibliography. Solutions to OddNumbered Exercises. Index: List of Symbols Index: Alphabetical Listing. Catalog no. C8328, 2010, 440 pp. ISBN: 978-1-4200-8328-6, $89.95
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Algebraic Number Theory Second Edition
“This is a remarkable book that will be a valuable reference for many people, including me. The book shows great care in preparation, and the ample details and motivation will be appreciated by lots of students. The solid punches at the end of each chapter will be appreciated by everybody. It deserves success with many adoptions as a text.” —Irving Kaplansky, Mathematical Sciences Research Institute
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat’s Last Theorem (FLT) and consequences of the ABC conjecture, including Thue–Siegel–Roth theorem, Hall’s conjecture, the Erdös–Mollin–Walsh conjecture, and the Granville–Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes’, Selberg’s, Linnik’s, and Bombieri’s sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring.
Selected Contents Integral Domains, Ideals, and Unique Factorization. Field Extensions. Class Groups. Applications: Equations and Sieves. Ideal Decomposition in Number Fields. Reciprocity Laws. Appendices. Bibliography. Solutions to Odd-Numbered Exercises. Index. Catalog no. K12056, January 2011, 442 pp. ISBN: 978-1-4398-4598-1, $89.95
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Numerical, Real, Complex and Functional Analysis Classical and Modern Numerical Analysis Theory, Methods and Practice Azmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, and Padmanabhan Seshaiyer Series: Chapman and Hall/CRC Numerical Analysis and Scientific Computation Series
Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.
Selected Contents Mathematical Review and Computer Arithmetic. Numerical Solution of Nonlinear Equations of One Variable. Numerical Linear Algebra. Approximation Theory. Eigenvalue-Eigenvector Computation. Numerical Differentiation and Integration. Initial Value Problems for Ordinary Differential Equations. Numerical Solution of Systems of Nonlinear Equations. Optimization. Boundary Value Problems and Integral Equations. Appendix. References. Index.
Understanding Real Analysis Paul Zorn “This is a textbook designed to teach students who are new to analysis what it’s all about. ... The path Zorn takes is based on several very reasonable principles. These include: building on calculus basics; focusing on mathematical proof, structure and language; staying with the basics; offering many examples and many solved exercises; and gradually increasing technical sophistication. ... There are plenty of exercises. They tend to follow a pattern where an exercise that is not completely straightforward is broken into multiple parts to guide the student to a solution.” —Bill Satzer, MAA Reviews, June 2010
The author's primary aims are to develop ideas already familiar from elementary calculus in a rigorous manner and to help students deeply understand some basic but crucial mathematical ideas and to see how definitions, proofs, examples, and other forms of mathematical "apparatus" work together to create a unified theory. A key feature of the book is that it includes substantial treatment of some foundational material, including general theory of functions, sets, cardinality, and basic proof techniques.
Selected Contents Preliminaries: Numbers, Sets, Proofs, and Bounds Sequences and Series Limits and Continuity Derivatives Integrals Solutions Catalog no. K00535, 2010, 362 pp. ISBN: 978-1-56881-415-5, $49.00
Catalog no. C9157, 2010, 628 pp. ISBN: 978-1-4200-9157-1, $102.95
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Numerical, Real, Complex and Functional Analysis Real and Complex Analysis Christopher Apelian and Steve Surace Drew University, Madison, New Jersey, USA
Measure and Probability Siva Athreya Indian Academy of Sciences, Bangalore, India
V.S. Sunder
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Institute of Mathematical Sciences, Chennai, India
Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory at the same time. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide.
“This textbook is suitable for a one-semester course on measure theory and probability for beginning graduate students in mathematics, probability and statistics. It can also be used as a textbook for advanced undergraduate students in mathematics … The topics are well selected to meet the needs of students who are interested in graduate studies in areas related to analysis, probability, stochastic processes and statistics … This makes the book student-friendly. A motivated student can use it by him- or herself to learn the topics well.”
By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website. This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.
Features • Shows how real analysis and complex analysis are related • Highlights the differences between real and complex functions • Explains how the theory of complex integration leads to some of the most interesting and useful results in all of analysis • Contains more than 1,000 exercises, including embedded problems within the text and supplementary exercises at the end of each chapter
—Yimin Xiao, Mathematical Reviews, 2010
“… The book is neatly written and can be recommended as an introduction to all students who intend to start courses on advanced modern probability.” —EMS Newsletter, September 2009
This book covers the fundamentals of measure theory and probability theory. It begins with the construction of Lebesgue measure via Caratheodory’s outer measure approach and goes on to discuss integration and standard convergence theorems and contains an entire chapter devoted to complex measures, Lp spaces, Radon–Nikodym theorem, and the Riesz representation theorem. It presents the elements of probability theory, the law of large numbers, and central limit theorem. The book then discusses discrete time Markov chains, stationary distributions and limit theorems. The appendix covers many basic topics such as metric spaces, topological spaces and the Stone–Weierstrass theorem.
Selected Contents
• Offers hints and solutions to selected exercises as well as further reading suggestions on the book’s website
Probabilities and Measures. Integration. Random Variables. Probability Measures on Product Spaces. Characteristics and Convergences. Markov Chains. Some Analysis. Appendix. Tables. References. Index.
Catalog no. C8067, 2010, 567 pp. ISBN: 978-1-58488-806-2, $92.95
Catalog no. N10021, 2009, 232 pp. ISBN: 978-1-4398-0126-0, $71.95
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Numerical, Real, Complex and Functional Analysis
Applied Functional Analysis Second Edition J. Tinsley Oden and Leszek F. Demkowiccz University of Texas at Austin, USA
Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. It presents the mathematical foundations that lead to classical results in functional analysis. More specifically, the text prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods. While retaining the structure of its best-selling predecessor, this second edition includes revisions of many original examples, along with new examples that often reflect the authors’ own vast research experiences and perspectives. This edition also provides many more exercises as well as a solutions manual for qualifying instructors. Each chapter begins with an extensive introduction and concludes with a summary and historical comments that frequently refer to other sources.
New to the Second Edition • Completely revised section on limit superior and limit inferior • New discussions of connected sets, probability, Bayesian statistical inference, and the generalized (integral) Minkowski inequality • New sections on elements of multilinear algebra and determinants, the singular value decomposition theorem, the Cauchy principal value, and Hadamard finite part integrals • New example of a Lebesgue non-measurable set Ideal for a two-semester course, this classroomtested textbook teaches students how to prove theorems and prepares them for rigorous study of more advanced mathematical topics.
Catalog no. C1956, 2010, 596 pp. ISBN: 978-1-4200-9195-3, $119.95
Features • Focuses on real analysis with special attention given to infinite-dimensional settings • Covers set theory, linear algebra, Lebesgue measure, Lebesgue integration theory, elementary topology, and the theory of metric spaces • Explores Banach and Hilbert spaces • Contains examples that motivate students to appreciate the value of mathematical rigor
Selected Table of Contents Preliminaries Elementary Logic and Set Theory. Relations. Functions. Cardinality of Sets. Foundations of Abstract Algebra. Elementary Topology in Rn. Elements of Differential and Integral Calculus. Linear Algebra Vector Spaces—The Basic Concepts. Linear Transformations. Algebraic Duals. Euclidean Spaces. Lebesgue Measure and Integration Lebesgue Measure. Lebesgue Integration Theory. Topological and Metric Spaces Elementary Topology. Theory of Metric Spaces. Banach Spaces Topological Vector Spaces. Hahn–Banach Extension Theorem. Bounded (Continuous) Linear Operators on Normed Spaces. Closed Operators. Topological Duals. Weak Compactness. Closed Range Theorem. Solvability of Linear Equations. Hilbert Spaces Basic Theory. Duality in Hilbert Spaces. Elements of Spectral Theory. References Solutions manual available for qualifying instructors
For more information and complete contents, visit www.crctextbooks.com
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Math for Biology Differential Equations and Mathematical Biology
NEW
Second Edition
Tel-Aviv University, Israel
D.S. Jones
Ron Unger
University of Dundee, Scotland
Bar-Ilan University, Ramat-Gan, Israel
Biological Computation Ehud Lamm
Michael Plank University of Canterbury, Christchurch, New Zealand
Series: Chapman & Hall/CRC Mathematical & Computational Biology
B.D. Sleeman
“I read this book in one breath—it opens vistas on how the fields of computation and biology can inspire each other. I particularly enjoyed the analogies between immune systems and software that fights computer viruses.”
University of Leeds, UK Series: Chapman & Hall/CRC Mathematical & Computational Biology
“…Much progress by these authors and others over the past quarter century in modeling biological and other scientific phenomena make this differential equations textbook more valuable and better motivated than ever. …The writing is clear, though the modeling is not oversimplified. Overall, this book should convince math majors how demanding math modeling needs to be and biologists that taking another course in differential equations will be worthwhile. The coauthors deserve congratulations as well as course adoptions.” —SIAM Review, Sept. 2010
“… Where this text stands out is in its thoughtful organization and the clarity of its writing. This is a very solid book … The authors succeed because they do a splendid job of integrating their treatment of differential equations with the applications, and they don’t try to do too much. … Each chapter comes with a collection of well-selected exercises, and plenty of references for further reading.“ —MAA Reviews, April 2010
Ideal for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, this bestselling text introduces the fundamental modeling and analytical techniques used to understand biological phenomena. It discusses the modeling of biological behavior, including biochemical reactions, nerve pulses, predator–prey models, and epidemics. This expanded edition includes a new section on spiral waves, recent developments in tumor biology, and additional examples and exercises. Providing downloadable MATLAB® files online, it presents numerical solutions of differential equations and numerical bifurcation analysis. Catalog no. C8357, 2010, 462 pp. ISBN: 978-1-4200-8357-6, $82.95
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—Uri Alon, Weizmann Institute of Science, Rehovot, Israel, and author of An Introduction to Systems Biology: Design Principles of Biological Circuits
“The book by Lamm and Unger methodically covers exciting developments in biological computation, offering for the first time a broad perspective of this important cutting-edge field of research.“ —Ehud Shapiro, The Harry Weinrebe Professorial Chair of Computer Science and Biology, Weizmann Institute of Science, Rehovot, Israel
“This is a wonderful treatise on bio-inspired computation, written from a computer science perspective. The authors are extremely knowledgeable about their subject, and the material they cover is both broad and deep. The book should benefit anyone interested in the connection between computer science and biology, a connection that is poised to become dramatically central to the science of the 21st century.” —David Harel, The William Sussman Professorial Chair, Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel
A unified overview of computer science ideas inspired by biology, Biological Computation presents the most fundamental and significant concepts in this area. In the book, readers discover profound ideas about computer science through biological examples, such as the use of DNA for performing computations and how evolution solves optimization problems. The text focuses on cellular automata, evolutionary computation, neural networks, and molecular computation. Catalog no. C7959, January 2011, 352 pp. ISBN: 978-1-4200-8795-6, $79.95
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Math for Biology NEW
An Introduction to Stochastic Processes with Applications to Biology Second Edition Linda J. S. Allen Texas Tech University, Lubbock, USA
An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and the genetics of inbreeding. Because of their rich structure, the text focuses on discrete and continuous time Markov chains and continuous time and state Markov processes.
New to the Second Edition • A new chapter on stochastic differential equations that extends the basic theory to multivariate processes, including multivariate forward and backward Kolmogorov differential equations and the multivariate Itô’s formula • The inclusion of examples and exercises from cellular and molecular biology • Double the number of exercises and MATLAB® programs at the end of each chapter • Answers and hints to selected exercises in the appendix • Additional references from the literature This edition continues to provide an excellent introduction to the fundamental theory of stochastic processes, along with a wide range of applications from the biological sciences. To better visualize the dynamics of stochastic processes, MATLAB programs are provided in the chapter appendices. Catalog no. K10993, January 2011, 490 pp. ISBN: 978-1-4398-1882-4, $89.95
Algorithms in Bioinformatics A Practical Introduction Wing-Kin Sung National University of Singapore Series: Chapman & Hall/CRC Mathematical & Computational Biology
"This aptly titled book is a timely publication that details several algorithms widely used in bioinformatics. … This work can serve as a reference guide for students and researchers attempting to implement or learn algorithms relevant to bioinformatics. Although some concepts referenced in the book specifically target advanced bioinformatics experts, general users should not be discouraged from reading this work. …Summing Up: Recommended." —CHOICE, June 2010
This classroom-tested text provides an in-depth introduction to the algorithmic techniques applied in bioinformatics. For each topic, the author clearly details the biological motivation, precisely defines the corresponding computational problems, and includes detailed examples to illustrate each algorithm. The text covers basic molecular biology concepts, sequence similarity, the suffix tree, sequence databases, sequence and genome alignment, the phylogenetic tree, genome rearrangement, motif finding, the secondary structure of RNA, peptide sequencing, and population genetics.
Features • Covers stochastic processes that occur in many biological applications, with an emphasis on Markov processes • Requires minimal mathematical and biological background • Contains examples and exercises from population, cellular, and molecular biology; epidemiology; drug kinetics and genetics • Includes answers and hints to selected exercises in the appendix Supplementary material is provided on the author’s website and a solutions manual is available for qualifying instructors Catalog no. C7033, 2010, 407 pp. ISBN: 978-1-4200-7033-0, $82.95
For more information and complete contents, visit www.crctextbooks.com
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Mathematics for Engineers, Physicists, and Scientists NEW
Advanced Engineering Mathematics with MATLAB® Third Edition Dean G. Duffy Former Instructor, US Naval Academy, Annapolis, Maryland, USA
Taking a practical approach to the subject, Advanced Engineering Mathematics with MATLAB®, Third Edition continues to integrate technology into the conventional topics of engineering mathematics. The author employs MATLAB to reinforce concepts and solve problems that require heavy computation. MATLAB scripts are available for download at www.crcpress.com. Along with new examples, problems, and projects, this updated and expanded edition incorporates several significant improvements.
New to the Third Edition • New chapter on Green’s functions • New section that uses the matrix exponential to solve systems of differential equations • More numerical methods for solving differential equations, including Adams–Bashforth and finite element methods • New chapter on probability that presents basic concepts, such as mean, variance, and probability density functions • New chapter on random processes that focuses on noise and other random fluctuations Suitable for a differential equations course or a variety of engineering mathematics courses, the text covers fundamental techniques and concepts as well as Laplace transforms, separation of variable solutions to partial differential equations, the z-transform, the Hilbert transform, vector calculus, and linear algebra. It also highlights many modern applications in engineering to show how these topics are used in practice A solutions manual is available for qualifying instructors Catalog no. K10835, January 2011, 1105 pp. ISBN: 978-1-4398-1624-0, $109.95
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MATLAB with Applications to Engineering, Physics and Finance David Baez-Lopez Universidad de las Américas, Puebla, Mexico
The mathematical software MATLAB® integrates computation, visualization, and programming to produce a powerful tool for a number of different tasks in mathematics. Focusing on the MATLAB toolboxes especially dedicated to science, finance, and engineering, MATLAB® with Applications to Engineering, Physics and Finance explains how to perform complex mathematical tasks with relatively simple programs. This versatile book is accessible enough for novices and users with only a fundamental knowledge of MATLAB, yet covers many sophisticated concepts to make it helpful for experienced users as well. The author first introduces the basics of MATLAB, describing simple functions such as differentiation, integration, and plotting. He then addresses advanced topics, including programming, producing executables, publishing results directly from MATLAB programs, and creating graphical user interfaces. The text also presents examples of Simulink® that highlight the advantages of using this software package for system modeling and simulation. The applications-dedicated chapters at the end of the book explore the use of MATLAB in digital signal processing, chemical and food engineering, astronomy, optics, financial derivatives, and much more.
Features • Brings together diverse applications of MATLAB in many areas, including industrial, civil, and mechanical engineering; kinematics; dynamics; electricity; modern physics; annuities; and Black–Scholes analysis • Contains more than 160 practical worked examples and numerous end-of-chapter exercises • Offers downloadable MATLAB examples and programs on the book’s website Catalog no. K10356, 2010, 426 pp. ISBN: 978-1-4398-0697-5, $82.95
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Mathematics for Engineers, Physicists, and Scientists Advanced Mathematical Methods in Science and Engineering Second Edition S.I. Hayek Pennsylvania State University, University Park, USA
“S.I. Hayek’s Advanced Mathematical Methods in Science and Engineering covers a wide range of applied mathematics centered around differential equations. … Hayek’s book contains a great deal of useful information …” —MAA Reviews, October 2010
This update of a best-selling text presents methods of applied mathematics that are particularly suited to address physical problems in science and engineering. This edition incorporates a new chapter that offers an extensive treatment of numerical methods. It also contains new appendices on vector algebra, calculus, and matrix algebra. The author provides a complete treatment of ODEs and PDEs, covers Green’s functions for unbounded and bounded media, and explores self-adjoint systems and orthogonal series. Numerous examples illustrate the various methods of solution and answers to the end-of-chapter problems are included at the back of the book.
Features • Incorporates a new chapter on numerical methods • Contains new appendices on vector algebra, calculus, and matrix algebra • Provides a complete treatment of ODEs and PDEs • Covers Green’s functions for unbounded and bounded media • Explores self-adjoint systems and orthogonal series
Mathematical Methods in Physics Partial Differential Equations, Fourier Series, and Special Functions Victor Henner, Tatyana Belozerova, and Kyle Forinash “[Henner, Forinash, and Belozerova] address the main topics of many courses in mathematical physics within the fields of engineering, physics, mathematics, and applied mathematics. The texbook and accompanying software is significantly more detailed than typical introductions to partial differential equations, they say, and provide examples on setting up physical problems as mathematical ones, solving partial differential equations under different types of boundary conditions, working with special functions, and carrying out a Fourier analysis using these functions. The software provides a simple interface, and does not require students to learn a programming language.” —Book News Inc., September 2009 This book is a text on partial differential equations (PDEs) of mathematical physics and boundary value problems, trigonometric Fourier series, and special functions. This is the core content of many courses in the fields of engineering, physics, mathematics, and applied mathematics. The accompanying software provides a laboratory environment that allows users to generate and model different physical situations and learn by experimentation. From this standpoint, the book along with the software can also be used as a reference book on PDEs, Fourier series and special functions for students and professionals alike.
Selected Contents
Ordinary Differential Equations. Series Solutions of Ordinary Differential Equations. Special Functions. Boundary Value Problems and Eigenvalue Problems. Functions of a Complex Variable. Partial Differential Equations of Mathematical Physics. Integral Transforms. Green’s Functions. Asymptotic Methods. Numerical Methods. Appendices. References. Answers. Index.
Fourier Series. Sturm-Liouville Theory. OneDimensional Hyperbolic Equations. TwoDimensional Hyperbolic Equations. OneDimensional Parabolic Equations. Parabolic Equations for Higher-Dimensional Problems. Elliptic Equations. Bessel Functions. Legendre Functions. Eigenvalues and Eigenfunctions of the Sturm-Liouville Problem Auxiliary Functions for Different Types of Boundary Conditions. The Sturm-Liouville Problem and the Laplace Equation. Vector Calculus. How to Use the Software Associated with this Book.
Catalog no. C1977, 2010, 866 pp. ISBN: 978-1-4200-8197-8, $129.95
Catalog no. K00437, 2009, 859 pp. ISBN: 978-1-56881-335-6, $115.00
Selected Contents
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Probability and Operations Research Linear and Nonlinear Programming with Maple
Introduction to Probability with Mathematica®
An Interactive, Applications-Based Approach
Second Edition
Paul E. Fishback
Kevin J. Hastings Knox College, Galesburg, Illinois, USA
Grand Valley State University, Allendale, Michigan, USA
Series: Textbooks in Mathematics
Series: Textbooks in Mathematics
"Introduction to Probability with Mathematica adds computational exercises to the traditional undergraduate probability curriculum without cutting out theory. … a good textbook for a class with a strong emphasis on hands-on experience with probability. … One interesting feature of the book is that each set of exercises includes a few problems taken from actuarial exams. No doubt this will comfort students who are taking a probability course in hopes that it will prepare them for an actuarial exam. Another interesting feature is the discussion of the Central Limit Theorem. The book goes into an interesting discussion of the history of the theorem … ."
Integrating a hands-on learning approach, a strong linear algebra focus, Maple™ software, and real-world applications, this text introduces the mathematical concepts and principles underlying linear and nonlinear programming. It draws on the simplex method to develop the major ideas of duality and sensitivity analysis and provides applications and exercises from zoology, chemistry, and game theory to illustrate how linear and nonlinear programming are invaluable problem solving tools. The text solves problems using Maple and includes explicit Maple instructions, important commands, and sample worksheets. Maple worksheets and code are available on the book’s website.
Features • Improves conceptual understanding and solves problems using Maple • Draws upon a partitioned matrix multiplication view of the simplex method to develop the major ideas of duality and sensitivity analysis • Provides a variety of applications and exercises from zoology, transportation, chemistry, genetics, game theory, and more to illustrate how linear and nonlinear programming are invaluable problem solving tools • Offers Maple worksheets and code on www.lp-nlp-with-maple.org/
Pedagogical Features • Assesses student understanding through "waypoints" that consist of simple computations or brief questions • Reinforces problem solving and mathematical communication skills with application projects that address real-world problems in transportation, work scheduling, cancer diagnosis, portfolio design, and predator-prey habitats
—MAA Reviews, December 2009
Updated to conform to Mathematica® 7.0, this second edition shows how to easily create simulations from templates and solve problems using Mathematica®. Along with new sections on order statistics, transformations of multivariate normal random variables, and Brownian motion, this edition offers an expanded section on Markov chains, more example data of the normal distribution, and more attention on conditional expectation. It also includes additional problems from Actuarial Exam P as well as new examples, exercises, and data sets. The accompanying CD-ROM contains updated Mathematica® notebooks and a revised solutions manual is available for qualifying instructors.
Selected Contents Discrete Probability. Discrete Distributions. Continuous Probability. Continuous Distributions. Asymptotic Theory. Stochastic Processes and Applications. Appendix. References. Index. Catalog no. C7938, 2010, 465 pp. ISBN: 978-1-4200-7938-8, $92.95
Catalog no. C064X, 2010, 413 pp. ISBN: 978-1-4200-9064-2, $92.95
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